1. Field of Invention
The invention generally relates to methods for obtaining, processing and displaying parameters associated with in vivo tissue water diffusion as pathologically significant images using magnetic resonance imaging. More particularly, the invention relates to methods for obtaining and processing diffusion weighted output signals from a magnetic resonance imaging apparatus, and to the fast creation of high definition images of internal bodily tissue(s) utilizing the so processed magnetic resonance output signals.
2. Summary of the Prior Art
Tissue differentiation and localization always have been basic goals of magnetic resonance imaging. Indeed, the desire to distinguish between normal tissue and tumor tissue using magnetic resonance imaging techniques was recognized at least thirty years ago. At that time, it was realized that the spin-lattice, so-called xe2x80x9cT1xe2x80x9d, as well as the spin-spin, so-called xe2x80x9cT2xe2x80x9d, relaxation parameters are different between normal and cancerous tissues. Accordingly, by appropriately mapping the various T1 and/or T2 relaxation times determined from magnetic resonance signals of various voxels in an anatomical slice of interest as relative image amplitudes, it was possible to create images generally showing the demarcation of tumor tissue from adjacent normal tissue.
In the intervening time period, methods of obtaining T1- or T2-weighted images using magnetic resonance imaging techniques have improved. In addition, a large amount of experience has been gained in the in vivo application of these methods in conjunction with the use of various paramagnetic contrast agents. In fact, the latter methodology has evolved to the point that presently the use of contrast agent enhanced T1- and/or T2-weighted imaging for the purpose of demarcating tissue boundaries is considered to be basically conventional. Nevertheless, the determination of tumor margins using this xe2x80x9cconventionalxe2x80x9d methodology still is not entirely successful.
More recently, diffusion-weighted magnetic resonance imaging has been proposed as a novel contrast mechanism for demarcating the boundaries of certain tumors. In this regard, so-called xe2x80x9capparent diffusion coefficientxe2x80x9d (ADC) maps seem to provide useful information about the structural details of tumors. Hence, there are reports in the literature that suggest that peritumoral edema, solid enhancing, solid necrotic non-enhancing and cystic parts of tumors can be recognized on ADC maps.
Still further, so-called xe2x80x9cdiffusion tensor imagingxe2x80x9d is believed to add information about the directional dependence of molecular diffusion that may prove to be helpful in the demarcation of tumor margins. Again, however, these methods, even when used in conjunction with contrast enhanced T1 and T2 relaxation-weighted imaging, are not totally successful.
To better understand the above concepts, and the acquisition and use of magnetic resonance measurements of in vivo diffusion as contemplated by the present invention, it will be instructive to first generally discuss some basics. First, the concepts of isotropic diffusion, the so-called xe2x80x9cdiffusion coefficientxe2x80x9d, and the measurement of the xe2x80x9cdiffusion coefficientxe2x80x9d with magnetic resonance will be presented in a generalized manner. Second, the concepts of the extension of the definition of diffusion to so-called xe2x80x9canisotropicxe2x80x9d diffusion, and the characterization of diffusion with a diffusion tensor, rather than a single coefficient, will be presented. Third, the effects of blood perfusion in the micro-circulatory system as causing deviations in expected magnetic resonance signal behavior will be discussed. Finally, the phenomenon of a departure from the normally adopted magnetic resonance signal behavior when the diffusion encoding range is extended substantially beyond the parameters currently in clinical use will lead to a discussion of the present invention.
First, with regard to isotropic diffusion and its measurement using magnetic resonance, it will be recognized that in a pure liquid such as water at room temperature, the individual water molecules are in constant motion due to the phenomenon of thermal agitation. This phenomenon is commonly referred to as xe2x80x9cBrownian motionxe2x80x9d. The so-called xe2x80x9cdiffusion coefficientxe2x80x9d (herein sometimes referred to as xe2x80x9cD xe2x80x9d) is a measure of this molecular motion, and it can be determined with magnetic resonance techniques.
More particularly, a magnetic field gradient can be used to xe2x80x9ctagxe2x80x9datomic level spins in a sample according to their location in space at the time of the application of a first magnetic gradient to the sample. A second gradient, applied at a later time, then serves to probe how far, on average, the individual spins have moved between the time of the first gradient application and the time of the second gradient application. In the ideal case, these magnetic field gradients are applied in brief, strong bursts separated by a common well-defined time period. In practice in clinical magnetic resonance systems, however, the gradients typically are applied for a moderate duration of several tens of milliseconds, and the leading edges of the respective bursts are separated by delays of a similar length of time.
Under these conditions, the diffusion encoding level, i.e., the so-called xe2x80x9cb-factorxe2x80x9d, is defined by the following relationship:
b=xcex32G2xcex42(xcex94xe2x88x92xcex4/3) 
where xcex3 is the gyromagnetic ratio (42.58 MHz/Tesla for protons), G is the gradient amplitude, xcex4 is the duration of each gradient lobe, and xcex94 is the separation between lobes. Thus, with one gradient pulse placed prior to and the other following the 180xc2x0 pulse of a spin echo sequence (90xc2x0 RF-TE/2-180xc2x0 RF-TE/2 - acquire), the signal S of the spin-echo measured at echo time TE for isotropic diffusion is given by the mono-exponential relationship:
S=S0 exp (xe2x88x92bD). 
In this relationship, S0 depends upon machine constants, the spin-spin relaxation time T2, the spin-lattice relaxation time T1 in any experiment that repeats measurements every repetition time period TR, and the spin density xcfx81. Specifically, the diffusion coefficient D may be measured by making multiple measurements of S as a function of b, plotting the natural logarithm of S vs. b and then performing a linear regression analysis whose slope provides the experimental measurement of D. The value of b is most conveniently varied by keeping the time delay fixed and incrementing the amplitude G of the magnetic field gradient.
As will be seen from FIG. 1, the logarithmic decay of signal intensity from neat solutions of water, ethanol and isopropanol as a function of b derived using a single column sampling technique on a clinical scanner follows a straight-line. This is indicative of mono-exponential decay above the respective baseline noise levels for each of the solutions. The water signal decays the fastest, thereby indicating that it has the highest diffusion coefficient. However, the actual diffusion coefficients measured from the slopes of the decays shown above the base line noise values are in excellent agreement with the published literature for all three samples. Hence, for isotropic diffusion, it may be said that the logarithm of the intensity of the magnetic resonance signal varies linearly with b above a given noise threshold.
Second, the extension of the foregoing concepts to the measurement of tissue water diffusion within the context of magnetic resonance imaging led to certain adjustments in the above-stated theory. Thus, it was quickly realized that in certain organs like the brain, preferred directions of water diffusion exist. More particularly, diffusion along one direction, as selected by the direction of the magnetic field gradient vector could be different than the diffusion along another direction. In the brain, this lack of isotropy of the diffusion coefficient (the so-called xe2x80x9cdiffusion anisotropyxe2x80x9d) was, and is, attributed to the presence of nerve fiber tracts along which water is more free to move than it is in directions perpendicular to these tracts.
Accordingly, there is reason to believe that tissue water diffusion cannot be characterized with a single diffusion coefficient D, as for neat liquids. Instead, tissue water diffusion apparently requires a more complex formalism in order to characterize it accurately. This more complex formalism has been found to be presentable using the concept of a diffusion tensor.
A 3xc3x973 matrix may represent the diffusion tensor. This may be accomplished with six independent elements. Indeed, in light of the phenomenon of restricted or anisotropic diffusion, it generally is agreed in the art that at least three directions of the diffusion sensitization gradient (which are independent of the preferred directional diffusion) should be sampled to generate trace images. These trace images are the sum of the diagonal elements of the diffusion tensor. Further, a minimum of 6 directions must be sampled for each voxel, if the full diffusion tensor is to be evaluated for potentially useful studies related to myelination development and brain micro-architecture.
Thus, the current trend in the clinical implementation of diffusion imaging is to sample multiple slices of the brain, each at a low and a high b-factor, the latter being typically on the order of about 1000 sec/mm2. This high b-factor sampling commonly is repeated for at least three, and up to six, directions of the diffusion sensitization gradient. Nevertheless, despite the additional complexity added by the diffusion tensor formalism, the logarithmic plot of signal decay versus b-factor is still seen to follow a substantially mono-exponential best-fit relationship.
Still other experiments, however, have suggested that the mono-exponential signal decay versus b-factor relationship just mentioned may not be necessarily accurate. Thus, studies of cat brain water diffusion have suggested that the signal decay variation with b-factor is a bi-exponential function over a limited b-factor range under 500 sec/mm2. This model, however, has been criticized.
Nevertheless, it appears to be true that the small amplitude, fast diffusing component of the bi-exponential function observed in the very low b-factor range may be attributable to perfusing blood. More specifically, blood in the micro-circulation has a very high diffusion coefficient that is not attributable to the normal, thermal Brownian motion associated with the remainder of the tissue water (i.e., water within and between the cells, but not in the vasculature). Consequently, there is a general consensus that there is indeed a small, very quickly diffusing component contributing to signal decay at low b-factors under 300 sec/mm2 in the brain. Diffusion coefficients determined by signal sampling at different b-factors between 0 and 1000 sec/mm2, therefore, are currently usually referred to as xe2x80x9capparent diffusion coefficientsxe2x80x9d (ADC), rather than more generically as diffusion coefficients D.
Prior to this invention, routine clinical magnetic resonance diffusion imaging of the brain was conducted at b-factors of between about 100 and 1000 sec/mm2. Average ADC maps then were generated on a pixel-by-pixel basis assuming that the xe2x80x9cbest-fitxe2x80x9d relationship between the magnetic resonance signal and the b-factor is a mono-exponential function (substantially as set forth above with regard to isotropic diffusion).
Still more recently, however, it has been reported that with single volume experiments in rat brains at very high b-factors (up to about 10,000 sec/mm2), the magnetic resonance signal to b-factor relationship also is better explained utilizing a bi-exponential relationship than utilizing a mono-exponential relationship. This suggestion is not as easily dismissed as the blood perfusion case discussed above wherein the overall effect is deemed to be negligible, due to the small blood volume fraction and to be limited to the b-factors under the 300 sec/mm2 range. Hence, if these findings are confirmed, it is expected that the clarity of differentiation of tissue types across an image of a given diffusion weighted magnetic resonance imaged anatomical sample slice may be improved significantly. At the time of the research leading up to the present invention, however, the practical utility of such confirmatory findings remained unclear.
Accordingly, it is an object of the present invention to provide a water diffusion based, in vivo, magnetic resonance imaging method for the visualization of various tissue pathologies within healthy tissue with greater definition, clarity and speed than has heretofore been possible.
It also is an object of the present invention to provide a method of tissue visualization that provides well-defined, non-invasive imaging without the need for contrast agents with their related complications and cost.
Further, it is an object of the present invention to provide a method of tissue visualization that results in images characterized by very well-defined tissue visualization characteristics using diffusion weighted magnetic resonance imaging on a substantially real-time basis at low cost.
These and other objects and advantages of the present invention arise from the fact that it now has been shown that diffusion-weighted magnetic resonance image signals taken over a wide b-factor range in fact are best described using the bi-exponential model:
S(b)=A1 exp (xe2x88x92ADC1b)+A2 exp (xe2x88x92ADC2b) 
This model is derived from the mono-exponential equation discussed above in connection with isotropic diffusion (a concept that will become significant below). In this equation ADC1, and ADC2 are apparent diffusion coefficients, and A1 and A2 are the respective amplitudes thereof. Also, the first term of the equation is known as the xe2x80x9cfastxe2x80x9d diffusing component, and the second term of the equation is known as the xe2x80x9cslowxe2x80x9d diffusing component.
This phenomenon is not yet fully understood. It, however, is consistent with a model wherein a pool of water with a very slow diffusion coefficient is located in an exchange relationship with a larger pool having a fast diffusion coefficient. The preferred so-called xe2x80x9cwidexe2x80x9d b-factor range according to the present invention has been determined to be between about 100 and about 5000 sec/mm2.
Therefore, in the preferred embodiment of the method of the present invention, a magnetic resonance imaging apparatus is provided that is capable of performing diffusion-weighted magnetic resonance imaging using b-factors in the range of between about 100 and about 5000 sec/mm2. This apparatus is used to generate image data across a selected anatomical slice at b-factors that are commonly equally spaced within the above stated range of b-factors, using at least one gradient direction.
Thus, the data acquired characterizes the diffusion-related signal decays according to a bi-exponential function on a pixel-by-pixel basis. Nevertheless, the method of the invention proceeds to determine the best fit of the diffusion-related decays to a mono-exponential function as discussed above with regard to the prior art. However, this determination is made not because it is believed that the best fit to the acquired data is a mono-exponential function. Instead, it is made to establish a pathologically significant frame of reference for use in association with the following steps of the method.
Thereafter, the x2 (chi2) error parameter associated with mono-exponential fits of the tissue water signal decays with N b-factors is determined according to the following relationship:       x    2    =            ∑              I        =        1            N        ⁢                  (                              S            I                    -                                    S              o                        ⁢            exp            ⁢                          xe2x80x83                        ⁢                          (                              -                                  ADCb                  I                                            )                                      )            2      
This chi2-error parameter constitutes a measure of the departure of the actual average signal decays from the best-fit mono-exponential behavior over the wide b-factor range employed. The amplitudes of these error parameters have been found to provide remarkably well-defined tumor pathology values characterized by extremely high signal-to-noise ratios. Hence, these error parameters then are used to form an image by setting a zero deviation from the mono-exponential behavior to correspond with a black pixel, and causing the brightness of the pixels to increase as the deviation from the predetermined best-fit mono-exponential behavior becomes larger.
Stated slightly differently, it now has been concluded that at least two ADC components are required to describe ADC decay behavior over wide b-factor ranges in adult human brains. This is significant because when the lower b-factor ranges of conventional diffusion-weighted magnetic resonance imaging were used, the best fit achievable to the data points generated was believed to be similar to that characteristic of isotropic diffusion in neat fluids. This, however, was known to be technically incorrect for the reasons discussed above.
The present invention essentially establishes an approximation using a mono-exponential fit of the signal characteristics of water diffusion in tissue measured at each point across the selected slice of brain tissue as a baseline. Then, the chi2 error parameter for each corresponding measured data point at each b-factor is determined relative to the so established artificial mono-exponential baseline. Thereafter, the amplitudes of these chi2 error parameters are utilized to create the desired image. Of course, the baseline also may be determined using the majority tissue type contained in the imaged slice, for example, white matter. In the latter case, the chi2-error parameter for each measured data point is compared with the chi2 error parameter so determined for the predominant tissue type in the imaged slice. This further refines the resultant image so as to delineate even more clearly the location and extent of tissue types different from the predominant tissue type measured across the slice.
This novel approach allows the present invention to provide the desired well defined, non-invasive imaging of tumor pathology without the use of complex and costly paramagnetic contrast agents common to T1-weighted imaging. It also allows each tissue structure to be differentiated from those around it. This is because each section of the resultant image depends upon the characteristic difference of diffusion in and among the cells of the particular tissue type(s) present against the background level of an effectively pure fluid-like diffusion coefficient defined at each point across the entire sample. Thus, there is provided an entirely new concept in the art, a concept that inherently simplifies the computational complexities involved such that desired resultant pathologically significant slice images may be obtained very quickly without the necessity of complex and time consuming data processing.